Can I sync all contacts and Mail (macOS) to iCloud?

An iCloud email address will synchronise with all your devices via iCloud.

See Set up iCloud Mail on all your devices

Note that services not provided by Apple are not connected to iCloud, but if they are IMAP mail services they will synchronise with their service provider such as Gmail.

iCloud Contacts on your Mac (and any iOS device) similarly synchronise via iCloud.

See Set up iCloud for Contacts on all your devices

and Keep your contacts up to date with iCloud.

The same caveat for Mail services not supplied by Apple applies to Contacts - you can have Gmail contacts in your Contact app but these do not report to your iCloud account.

Additionally, iCloud Mail accounts and iCloud Contacts can be used when you sign into your account at icloud.com

What other mail services do you have? If you have Gmail for example that will draw your Gmail email from Google. Choose Gmail when you add your email account. See Add email accounts in Mail on Mac

When adding your Contacts choose the relevant provider - see Add contacts from iCloud, Google, and more to Contacts on Mac

It helps if the mechanisms at work are clarified.

Email accounts are now normally IMAP - a protocol that leaves the email in place at its source - on gmail servers, or iCloud servers, or thunderbird, or anywhere else.com. Your 'email account' on different devices each interrogate for any changes, and bring them to the device.

iCloud merely provides another place to interrogate and 'synchronise' this data between the devices. If you are synching documents, for instance, the 'master'/first occurrence goes to an iCloud server, and other devices see the change and either download it, or indicate it to you on that local device.

The same thing is happening for contacts. Unless contacts are in a file that is mastered back to iCloud, you will continue to 'sync' back to the original source be it gmail or wherever. It's simpler and a touch more secure if you pick a contacts application and keep it as the primary source file.